Preprint B40/2010
Mathematical Methods in Finance: Real Options on Mean-Reverting Cash-Flow Processes

Diogo Pires

**Keywords: **
Real Options | Cash Flow Modeling | Mean Reverting Process

Corporations are often faced with the possibility of investing in specific projects that might impact on their cash flow. The Real Option Analysis approach became, in the last few years, an important instrument for managers to take investment decisions.
The Real Option approach consists in the analysis of contracts, using the same tools developed for financial derivative markets. In the case of stocks, the Black and Scholes model assumes that the underlying asset of the contract follows a Geometric Brownian Motion. Nevertheless, if we are interested in modeling the cash flow that arises from a project that might be negative, then a GBM cannot possibly be a good model. In this case we return to the Bachelier model (which pre-dated Black and Scholes by almost 100 years), and show that, together with some extensions, it yields consistent results. The approach was implemented computationally and numerical results are presented.